Finite Group Databasebeta

← #16021069

Subgroups — #16021069

Order 3328.

472 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127974C211yesmaximal, characteristic, complemented
2#13127973C211yesmaximal, characteristic, complemented
3#13117151C211yesmaximal, characteristic, complemented
4#13117150C212yesmaximal, complemented
5#13117147C212yesmaximal, complemented
6#13117144C212yesmaximal, complemented
7#13117143C211yesmaximal, characteristic, complemented
8C2×#11718111C211yesmaximal, characteristic, complemented
9D13×D32C212yesmaximal, complemented
10#13117131C211yesmaximal, characteristic, complemented
11C13×#2263C211yesmaximal, characteristic, complemented
12#11719474—21no—
13#11719462—21no—
14C13×#508C2211yescharacteristic, complemented
15C2×C13×D16C2211yescharacteristic, complemented
16#11718854—21no—
17#11718808—21no—
18#11718580C2212yescomplemented
19#11718575—22no—
20#11718573C2212yescomplemented
21#11718572—22no—
22D13×D16C2212yescomplemented
23D13×D16C2212yescomplemented
24#11718565C2211yescharacteristic, complemented
25C2×D208C2211yescharacteristic, complemented
26#11718562C2211yescharacteristic
27C13×SD64C2212yescomplemented
28C13×D32C2212yescomplemented
29C13×M64C2211yescharacteristic, complemented
30#11718114C2211yescharacteristic, complemented
31#11718113C2211yescharacteristic, complemented
32#11718112C2211yescharacteristic, complemented
33#11718111C2211yescharacteristic, complemented
34#11718111C2212yescomplemented
35#11718111C2212yescomplemented
36C2×#88034C2211yescharacteristic, complemented
37#11718041C2212yescomplemented
38D416C2212yescomplemented
39#11718039C2212yescomplemented
40D13×C32C2212yescomplemented
41#88256—41no—
42#88251—41no—
43C13×#135—21no—
44C2×C13×D8—21no—
45#88203—41no—
46#88186—41no—
47#88173—22no—
48#88168—42no—
49#88166—22no—
50#88165—42no—
51D8×D13—22no—
52D8×D13—22no—
53#88158—21no—
54C2×D104—21no—
55#88155D411yescharacteristic
56C13×Q32C2311yescharacteristic
57C13×SD32—21no—
58C13×D16—21no—
59C13×D16C2311yescharacteristic
60C13×D16C2312yes—
61C2×C13×C16C2311yescharacteristic
62#88068—22no—
63#88067—22no—
64#88066—22no—
65#88066—22no—
66#88052D411yescharacteristic
67Dic104C2311yescharacteristic
68#88040—21no—
69D208—21no—
70D208C2311yescharacteristic
71D208C2312yes—
72#88038D412yes—
73C16×D13C2312yes—
74C13×C32C2312yes—
75#88034C2311yescharacteristic
76#88034C2311yescharacteristic
77#33982—131nomaximal, Sylow
78C13×#41—41no—
79C2×D4×C13—41no—
80C2×C22⋊D13—82no—
81#6131—42no—
82#6129—42no—
83#6129—81no—
84D4×D13—42no—
85D4×D13—42no—
86D4×D13—82no—
87D4×D13—81no—
88#6127—41no—
89#6127—81no—
90#6127D811yescharacteristic
91C2×D52—41no—
92C2×D52—81no—
93C13×Q16—21no—
94C13×SD16—41no—
95C13×D8—21no—
96C13×D8—22no—
97C13×D8—41no—
98C2×C8×C13C2×D411yescharacteristic
99#6106—42no—
100#6105—42no—
101#6104—42no—
102#6104—42no—
103#6099D811yescharacteristic
104Dic52—21no—
105D104—21no—
106D104—22no—
107D104—41no—
108#6095—41no—
109#6094D812yes—
110C8×D13C2×D412yes—
111C13×C16C2×D411yescharacteristic
112C13×C16C2411yescharacteristic
113#6090C2×D412yes—
114#3415—131no—
115#3415—131no—
116#2263—132no—
117#2263—132no—
118#2263—131no—
119#2263D1311yescharacteristic, complemented
120#2262—131no—
121#2262—132no—
122C2×D32—131no—
123C2×D32—132no—
124#2258—131no—
125C23×C13—81no—
126C22×D13—81no—
127C22×D13—82no—
128C22×D13—82no—
129Q8×C13—41no—
130D4×C13—41no—
131D4×C13—42no—
132D4×C13—81no—
133D4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13C2×D811yescharacteristic
136C22⋊D13—81no—
137C22⋊D13—82no—
138C22⋊D13—82no—
139C22⋊D13—82no—
140C22⋊D13D1612yes—
141C2×Dic13—82no—
142D52—41no—
143D52—42no—
144D52—82no—
145D52—81no—
146D52D1611yescharacteristic
147C4×D13—81no—
148C4×D13—82no—
149C4×D13C2×D812yes—
150Dic26—41no—
151Dic26D1611yescharacteristic
152C8×C13C2×D811yescharacteristic
153C8×C13C22×D411yescharacteristic
154#1055C2×D812yes—
155#576—261no—
156#576—261no—
157#509—262no—
158#509—262no—
159#509—261no—
160#509—261no—
161#508—132no—
162#508—132no—
163#508—131no—
164#508C2×D1311yescharacteristic, complemented
165C2×D16—132no—
166C2×D16—132no—
167C2×D16—131no—
168C2×D16C2×D1311yescharacteristic, complemented
169#504—131no—
170Q64—131no—
171SD64—131no—
172SD64—131no—
173SD64—132no—
174SD64C2×D1312yescomplemented
175D32—132no—
176D32—131no—
177D32—132no—
178D32—132no—
179D32C2×D1312yescomplemented
180M64—132no—
181M64C2×D1311yescharacteristic, complemented
182C2×C32—131no—
183C2×C32—132no—
184C22×C13—82no—
185C22×C13—81no—
186C22×C13—321no—
187C22×C13C2×D1611yescharacteristic
188C2×D13—82no—
189C2×D13—81no—
190C2×D13—322no—
191C2×D13—322no—
192C2×D13—321no—
193C2×D13C2×D1612yes—
194C4×C13—81no—
195C4×C13C2×D1611yescharacteristic
196C4×C13C22×D811yescharacteristic
197Dic13—81no—
198Dic13C2×D1612yes—
199H(5,𝔽2)—521no—
200H(5,𝔽2)—521no—
201AGL(1,ℤ/8)—522no—
202AGL(1,ℤ/8)—522no—
203AGL(1,ℤ/8)—521no—
204AGL(1,ℤ/8)—521no—
205#135—21no—
206#135—262no—
207#135—262no—
208#135—261no—
209C2×D8—21no—
210C2×D8—262no—
211C2×D8—262no—
212C2×D8—261no—
213#131—131no—
214Q32—131no—
215Q32C22×D1311yescharacteristic
216SD32—21no—
217SD32—262no—
218SD32—262no—
219SD32—261no—
220D16—21no—
221D16—132no—
222D16—131no—
223D16—262no—
224D16—262no—
225D16—261no—
226D16C22×D1312yes—
227D16C22×D1311yescharacteristic
228M32—131no—
229M32—132no—
230C2×C16—132no—
231C2×C16C22×D1311yescharacteristic
232C32—131no—
233C32—131no—
234C32C22×D1312yes—
235C2×C13—21no—
236C2×C13—161no—
237C2×C13—162no—
238C2×C13C22×D1611yescharacteristic
239D13—22no—
240D13—162no—
241D13—161no—
242#41—41no—
243#41—131no—
244#41—522no—
245#41—522no—
246#41—521no—
247#41—1041no—
248#41—1041no—
249C2×D4—41no—
250C2×D4—522no—
251C2×D4—522no—
252C2×D4—521no—
253C2×D4—1041no—
254C2×D4—1042no—
255C2×D4—1041no—
256C2×D4—1042no—
257Q16—21no—
258Q16—261no—
259SD16—41no—
260SD16—522no—
261SD16—522no—
262SD16—521no—
263D8—22no—
264D8—21no—
265D8—41no—
266D8—261no—
267D8—262no—
268D8—522no—
269D8—522no—
270D8—521no—
271M16—131no—
272M16—132no—
273C2×C8—132no—
274C2×C8D4×D1311yescharacteristic
275C16—132no—
276C16D4×D1311yescharacteristic
277C16C23×D1311yescharacteristic
278C13#3398211yescharacteristic, complemented, Sylow
279C23—81no—
280C23—1042no—
281C23—1042no—
282C23—1041no—
283Q8—41no—
284Q8—131no—
285Q8—521no—
286D4—42no—
287D4—41no—
288D4—81no—
289D4—81no—
290D4—132no—
291D4—131no—
292D4—521no—
293D4—522no—
294D4—1042no—
295D4—1042no—
296D4—1042no—
297D4—1042no—
298D4—1041no—
299D4—1041no—
300C2×C4—81no—
301C2×C4—132no—
302C2×C4—1042no—
303C2×C4—1042no—
304C2×C4—1041no—
305C2×C4D8×D1311yescharacteristic
306C8—132no—
307C8D8×D1311yescharacteristic
308C8C2×D4×D1311yescharacteristic
309C22—81no—
310C22—82no—
311C22—132no—
312C22—321no—
313C22—1042no—
314C22—1041no—
315C22—4161no—
316C22—4162no—
317C22—4162no—
318C22D13×D1611yescharacteristic
319C4—81no—
320C4—132no—
321C4—1041no—
322C4D13×D1611yescharacteristic
323C4C2×D8×D1311yescharacteristic
324C2—21no—
325C2—162no—
326C2—161no—
327C2—262no—
328C2—2082no—
329C2—2081no—
330C2C2×D13×D1611yescharacteristic
subgroupG/H
centerC2C2×D13×D16
commutator, cosocleC13×C16C24
FrattiniC16C23×D13
FittingC13×#2263C2
socleC2×C13C22×D16
hypercenter#2263D13
hypocenterC13#33982
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2263

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13127974C2semidirect
2. #13127973C2semidirect
3. #13117151C2semidirect
4. #13117150C2semidirect
5. #13117147C2semidirect
6. #13117144C2semidirect
7. #13117143C2semidirect
8. C2×#11718111C2semidirect
9. D13×D32C2semidirect
10. #13117131C2semidirect
11. C13×#2263C2semidirect
14. C13×#508C22semidirect
15. C2×C13×D16C22semidirect
18. #11718580C22semidirect
20. #11718573C22semidirect
22. D13×D16C22semidirect
23. D13×D16C22semidirect
24. #11718565C22semidirect
25. C2×D208C22semidirect
27. C13×SD64C22semidirect
28. C13×D32C22semidirect
29. C13×M64C22semidirect
30. #11718114C22semidirect
31. #11718113C22semidirect
32. #11718112C22semidirect
33. #11718111C22semidirect
34. #11718111C22semidirect
35. #11718111C22semidirect
36. C2×#88034C22semidirect
37. #11718041C22semidirect
38. D416C22semidirect
39. #11718039C22semidirect
40. D13×C32C22semidirect
119. #2263D13semidirect
164. #508C2×D13semidirect
168. C2×D16C2×D13semidirect
174. SD64C2×D13semidirect
179. D32C2×D13semidirect
181. M64C2×D13semidirect
278. C13#33982semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131279742
#131279732
#131171512
#131171502
#131171472
#131171442
#131171432
C2×#117181112
D13×D322
#131171312
C13×#22632
#3398213